Principles
Four rules govern everything on this site.
- No invented data. Every resistance, reactance and ampacity value is either taken from a published table and cited, or computed from a stated physical constant with the method shown. Nothing is estimated to fill a gap.
- The working is always visible. Every result shows the formula, the values substituted into it, and the intermediate steps. If a result looks wrong, you can find out where it went wrong rather than taking it on faith.
- Engineering and code stay separate. A voltage drop calculation is arithmetic. An ampacity figure is a table look-up. Neither is a compliance determination, and the tools never present one as the other.
- Assumptions are shown next to the result. When a calculation leaves something out (reactance, temperature, stranding), it says so on the same screen as the number, not in a footnote somewhere else.
Data sources
Conductor resistance, AWG and kcmil
NFPA 70, Chapter 9, Table 8, "Conductor Properties". Direct-current resistance at 75 °C (167 °F) in ohms per 1000 ft, calculated per National Bureau of Standards Handbook 100 (1966) and Handbook 109 (1972), at 100% IACS for copper and 61% IACS for aluminium.
AC resistance and reactance
NFPA 70, Chapter 9, Table 9, "Alternating-Current Resistance and Reactance for 600-Volt Cables, 3-Phase, 60 Hz, 75 °C, Three Single Conductors in Conduit". Ohms to neutral per 1000 ft for Class B stranded RHH in a cradled configuration. Capacitive reactance is ignored as negligible at these voltages.
Ampacity
NFPA 70, Table 310.16. Allowable ampacities of insulated conductors rated up to 2000 V, not more than three current-carrying conductors in a raceway, cable or earth, at 30 °C (86 °F) ambient. Correction and adjustment factors are not applied.
Conductor resistance, metric mm² sizes
Computed as R = ρ₂₀ × [1 + α₂₀ × (T − 20)] ÷ A, with ρ₂₀ = 1.7241 × 10⁻⁸ Ω·m for copper (100% IACS) and 2.8264 × 10⁻⁸ Ω·m for aluminium (61% IACS). Reproduces the NEC Table 8 solid-conductor values to within 0.2%.
Metric conductor sizes are the one place on this site where the numbers are computed rather than tabulated, because no published table used here covers IEC sizes. Every metric figure is labelled as calculated wherever it appears, and the derivation is below rather than hidden.
- ρ₂₀
- Resistivity at 20 °C · 1.7241e-8 Ω·m Cu, 2.8264e-8 Ω·m Al
- α₂₀
- Temperature coefficient at 20 °C · 0.00393 Cu, 0.00403 Al
- A
- Nominal cross-sectional area · m²
- T
- Conductor temperature · °C
What is assumed
| Assumption | Detail |
|---|---|
| Temperature | 75 °C unless you change it. The correction to any other temperature is R₂ = R₁ × [1 + α × (T₂ − 75)], with α of 0.00323 for copper and 0.00330 for aluminium, as published in NEC Chapter 9 Table 8 Note 2. Reactance is treated as temperature-independent. |
| Stranding | Class B stranded by default, which matches the basis of the AC table. Solid values are available for the sizes the table lists both ways; the difference is about 2%. |
| Frequency | 60 Hz for all reactance values. At 50 Hz, inductive reactance is about 17% lower: multiply by 50/60. Resistance is essentially unchanged. |
| Three-phase balance | Balanced load, equal current in all three phases at 120°. The result is the line-to-line voltage drop. An unbalanced system puts current in the neutral, which this does not model. |
| Parallel conductors | Assumed identical in size, material and length, so current divides evenly. Impedance divides by the number of sets. |
| Length | Every formula takes the one-way distance from source to load. The 2 or √3 multiplier accounts for the return path. A round-trip entry is halved first. |
| Effective impedance | Z_e = R cos θ + X_L sin θ, per NEC Chapter 9 Table 9 Note 2. Capacitive reactance is ignored, as it is negligible at these voltages. |
| Supply voltage | Taken as the nominal figure you enter, with no allowance for utility variation or source impedance. |
What is not modelled
A calculation describes an ideal conductor between two points. Real installations contain a great deal this does not account for:
- Terminations, splices and device contacts. Every joint has resistance. A good one contributes little; a poor one can dominate the whole run. This is precisely what a voltage drop test finds and a calculation cannot.
- Skin and proximity effect beyond the published data. The Table 9 AC resistance values already include these at 60 Hz for the geometries the table covers. Outside that (higher frequencies, other configurations) the data no longer applies.
- Harmonic currents. Non-linear loads produce currents at multiples of the supply frequency, where reactance is higher. A measured drop on a harmonic-rich circuit will exceed the fundamental-frequency calculation.
- Unbalanced three-phase and neutral current. The √3 multiplier assumes balance.
- Source impedance. The supply itself sags under load. This models the conductors only.
- Motor starting. Inrush current is several times running current, so the drop during a start is several times the steady-state figure. Enter the starting current if that is the case you care about.
- Voltage-drop provisions in specific NEC articles. Some installations and equipment carry mandatory voltage-drop requirements. Nothing here checks those.
How the engine is tested
The calculation code is a separate module from the interface, with no DOM access and no formatting decisions in it, so it can be tested directly rather than through the screen. The suite covers:
- Hand-calculated reference cases for DC, single-phase and three-phase, checked to six decimal places.
- The published effective-impedance column of NEC Chapter 9 Table 9. That table gives R, X and an effective Z at 0.85 power factor. Recomputing the third from the first two with our own formula and landing on the published value, across eleven size and raceway combinations, is the strongest available check that the impedance maths is right.
- Cross-method agreement. Results are compared against the circular-mil K-constant method, which uses entirely different inputs and must agree to within 1%.
- The resistivity model against the published table: the check described above, to within 0.5%.
- Round-trip consistency. The maximum-length answer is fed back through the forward calculation and must land exactly on the limit.
- Invariants across the whole size range. Resistance decreases monotonically with area; aluminium always exceeds copper; no combination of inputs produces NaN or Infinity; drop scales linearly with current and length.
- Validation behaviour for zero, negative, non-numeric, out-of-range and missing values.
Precision and rounding
Calculations run at full double precision throughout; rounding happens only at display. Voltages and percentages are shown to two decimal places, resistance to four significant figures, more than any of the source tables publish.
That precision describes the arithmetic, not the world. The underlying table values are themselves rounded, real conductors vary within manufacturing tolerance, and the current and length you entered are estimates. A result of 3.47% is not meaningfully different from one of 3.5%. Treat the second decimal place as a convenience for comparing two options, not as a claim about a physical circuit.
What this site is not
Corrections
If a number on this site is wrong, that is worth fixing and worth knowing about. See the contact page. Reports that identify the specific value and what it should be, with a source, get acted on fastest.